A ,man wishing to cross a river flowing with velocity u jumps at an angle theta with the river flow. (a) Find the net velocity of the man with respect to ground if he can swim with speed v in still water. (b) In what direction does the boat actually move ? ( c) Find how far from the point directly opposite to the starting point does the boat reach the opposite bank, if the width of the river is d.
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Given A ,man wishing to cross a river flowing with velocity u jumps at an angle theta with the river flow. (a) Find the net velocity of the man with respect to ground if he can swim with speed v in still water. (b) In what direction does the boat actually move ? ( c) Find how far from the point directly opposite to the starting point does the boat reach the opposite bank, if the width of the river is d.
- Now there is a river, so the man from the river at angle theta is jumping.
- So velocity of man with respect to river is V and velocity of river V r = u
- So velocity of man w.r.t river will be = velocity of man – velocity of river.
- Velocity of man = velocity of man w.r.t river + velocity of river.
- = V cos theta i + v sin theta j + u i
- = (Vcos theta + u) i + V sin theta j
- So velocity of man = √ (v cos theta + u)^2 + (v sin theta)^2
- = √v^2 sin^2 theta + v^2 cos ^2 theta + u^2 + 2 v u cos theta.
- = √v^2 + u^2 + 2 u v cos^2 theta.
- Now tan φ = Vy / Vx = V sin theta / V cos theta + u
- Or φ = V cos^-1 (V sin theta / V cos theta + u)
- So drift x = (v cos theta + u)t (t = d / v sin theta)
- = (v cos theta + u) d / v sin theta
- = d ( u + v cos theta ) / v sin theta
Reference link will be
https://brainly.in/question/12201153
https://brainly.in/question/4498633
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